Despite the elegancy of the PINN approach, the method is known to be prone to failures, especially when the solution interval is too large [1]}. We can illustrate this problem using two examples: solving a convection equation (REF )–() for \(\beta =20\) , \(t \in [0, 4]\)  and a reaction-diffusion equation (REF )–() for \(\rho =5\) , \(\nu =3\) , \(t \in [0, 1]\) . Fig. REF  shows the ground-truth solutions of the equation (first column) and inaccurate solutions found by PINNs (second column). The presented PINN solutions can be seen as combinations of two solutions: the correct solution near the initial conditions (for small \(t\) ) and a simpler solution farther away from the initial conditions (for large \(t\) ).
The third column in Fig. REF  illustrates that the second, simpler solution satisfies well the solved PDEs.
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